Lower Bounds for n -Term Approximations of Plane Convex Sets and Related Topics

Abstract

In this paper, we establish lower bounds for n-term approximations in the metric of L 2(I 2 ) of characteristic functions of plane convex subsets of the square I 2 with respect to arbitrary orthogonal systems. It is shown that, as n→∞, these bounds cannot decrease more rapidly than $$1/n$$ .